I'll start this out backwards - I solved the problem ultimately by turning the master volume all the way up and down, up and down. That was the easy bit!
The harder thing is explaining everything that led up to me solving the problem. There are too many variables to easily lay out here - I moved my home studio from one room to another, for a start, in my typically haphazard way. I plugged the P6 into my MBox2 via MIDI for the first time, messing about with the Novation X-Station as master keyboard, but this didn't suit so I moved on. I was doing various pluggings and un-pluggings when at some point I started hearing white noise from the output of the P6. Not in headphones, but either through the Mackie mixer or alternately, directly into the MBox. I found something on a forum suggesting switching from USB control to MIDI and this worked at first. But the noise returned and all my Global on/offing made no difference. I'd never had a problem with noise like this before with the synth, and was convinced it was somehow to do with the messing about with MIDI, something I'm quite naive about. When I finally pulled a MIDI cable out of the socket, the noise stopped again. But returned later! This went on - I tried swapping cables, but that wasn't it. The noise was still there even when the synth was turned off. As I said at the beginning, it all stopped finally when I turned the volume all the way up and down a few times. The noise sorta faded back in again, then out, but did disappear and hasn't been back for hours now.
Long story short, I know that USB connections can bring noise like this - I stopped using my Novation as a sound generator cos the noise was too much, so it's only a controller these days. And I haven't bothered with the P6 and USB since the first week I had the machine. But anyone have a clue why the P6 held on so long to the noise, even after I'd unplugged the MIDI cable and turned the unit off? Oh, I should mention that when I had the P6 hooked up to the MBox2 and was running a few MIDI patterns in Pro Tools, the P6 was doing various odd things. The volume would drop, or Slop would kick in at 100%, among.
Bit rambly here - sorry for that, but I'm grateful the noise seems to have been vanquished. Still no idea what this was all about. Clues?